Datalab quiz workings

question-13.R

install.packages('pracma')

mb <- rbind(
  c(1,1,0,0),
  c(0,0,1,1),
  c(1,0,1,0),
  c(0,1,0,1)
)

b <- c(24, 14, 26, 12, 12, 29, 11, 30, 12)
z <- matrix(0,4,4)

B <- rbind(
  cbind(mb, z),
  cbind(z, mb),
  c(1,0,0,0,1,0,0,0)
)
colnames(B) <- paste(
  rep('x', 8),
  rep(c(0, 1), each=4),
  rep(c(0, 1), each=2, times=2),
  rep(c(0, 1), times=4), sep='')
rres <- pracma::rref(cbind(B, b))
rres <- rres[1:7,]

tester <- function(val) {
  # I looked at rres to determine this next line
  c(rres[,9] - val * rres[,8], val)
}

res <- sapply(1:max(b), tester)
res <- res[,apply(res, 2, function(x) all(x >= 0))]
print(res)

question-15.R

o.r <- function(n, e) {
  for(a in 1:(n-1)) {
    for(b in 1:15) {
      res <- (a/(n-a))/(b/(16-b))
      if(res > e-.1 && res < e+.1) {
        cat(c(n, a, b, res), sep=', '); cat('\n')
      }
    }
  }
}

o.r(35, 1.42)
o.r(27, 1.67)
o.r(6, 1.49)